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Opposite & Adjacent Sides in a Right Angled Triangle

If E is a poi...

Question

If E is a point on side CA of an equilateral triangle ABC such that BE ⊥ CA, then AB² + BC² + CA² =

(a) 2 BE²
(b) 3 BE²
(c) 4 BE²
(d) 6 BE²

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Solution

In triangle ABC, E is a point on AC such that .

We need to find .

Since , CE = AE = $\frac{A C}{2}$ (In a equilateral triangle, the perpendicular from the vertex bisects the base.)

In triangle ABE, we have

Since AB = BC = AC

Therefore,

Since in triangle BE is an altitude, so

Hence option (c) is correct.

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